Ajax, jQuery and WordPress

Wrap your javascript code with document.ready, and if it works I would suggest going back to putting this in an external file

jQuery(document).ready(function(){
    jQuery('#ajax_form').on('submit', function(e) {
        e.preventDefault();
        console.log('Here');
        var form = jQuery('#ajax_form');
        var data = form.serialize();
        data.action = 'add_word_to_form'
        jQuery.post('/wp-admin/admin-ajax.php', data, function(response) {
            alert(data);           
        });
        //return false;
    });
});